Question

if the product of two numbers is 1080 And there LCM is 36 find there HCF​

Answer 1

$lcm \times hcf = product \: of \: two \: numbers$

lcm =36

36×HCF = 1080

HCF =1080÷36

HCF =30

Answer 2

• The highest common factor (H.C.F.) = 30.

Given :

• The product of two numbers = 1080.
• The least common multiple (L.C.M.) = 36.

To Find :

• The highest common factor (H.C.F.).

Solution :

Let,

The highest common factor (H.C.F.) be x.

We know that,

L.C.M. × H.C.F. = One number × Other number

• One number × Other number = Product of two numbers.

We have,

• Product of two numbers = 1080.
• Lease common multiple (L.C.M.) = 36.

So,

$\implies 36 \times x = 1080$

$\implies x = \cancel \dfrac{1080}{36}$

$\implies x = \cancel\dfrac{540}{18}$

$\implies x = \cancel \dfrac{270}{9}$

$\implies x = \cancel\dfrac{90}{3}$

$\implies x = \dfrac{30}{1}$

$\implies x = 30$

Hence,

The highest common factor (H.C.F.) is 30.

Verification :

We know that,

L.C.M. × H.C.F. = One number × Other number

• One number × Other number = Product of two numbers.

Now we have,

• Product of two numbers = 1080.
• Lease common multiple (L.C.M.) = 36.
• Highest common factor (H.C.F.) = 30.

So,

$\implies 36 \times 30 = 1080$

$\implies 1080 = 1080$

Hence Verified !!